Revealing mistake: At the beginning of the episode, MP Jim Hacker's chauffeur is driving him across London. You can see in the background that the car is moving around London, but the chauffeur is not driving it. You can't see his hands and the steering wheel never moves.

Deliberate mistake: In the scene where the ministers are all crammed into the train carriage if you look over Jim's shoulder there is a sign ("Notice" "In case of Fire" etc), while the headers are in English the actually paragraphs are written in gibberish.